{
  "id": "2208.03912",
  "version": "v1",
  "published": "2022-08-08T04:32:05.000Z",
  "updated": "2022-08-08T04:32:05.000Z",
  "title": "On oriented $m$-semiregular representations of finite groups",
  "authors": [
    "Jia-Li Du",
    "Yan-Quan Feng",
    "Sejeong Bang"
  ],
  "comment": "15pages, 6 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "A finite group $G$ admits an {\\em oriented regular representation} if there exists a Cayley digraph of $G$ such that it has no digons and its automorphism group is isomorphic to $G$. Let $m$ be a positive integer. In this paper, we extend the notion of oriented regular representations to oriented $m$-semiregular representations using $m$-Cayley digraphs. Given a finite group $G$, an {\\em $m$-Cayley digraph} of $G$ is a digraph that has a group of automorphisms isomorphic to $G$ acting semiregularly on the vertex set with $m$ orbits. We say that a finite group $G$ admits an {\\em oriented $m$-semiregular representation} if there exists a regular $m$-Cayley digraph of $G$ such that it has no digons and $G$ is isomorphic to its automorphism group. In this paper, we classify finite groups admitting an oriented $m$-semiregular representation for each positive integer $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-08T04:32:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semiregular representation",
      "cayley digraph",
      "oriented regular representation",
      "automorphism group",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}